If you are looking to have a commercial auto insurance policy cover your family, the answer to this is a very qualified yes. The qualification comes from the fact that the vehicle covered by the commercial insurance policy would have to be used primarily for business purposes, and only incidentally for family purposes. In other words, the only way that this can happen is that your car is involved in an accident while you are working or on the way to or from an appointment with family members in the vehicle. Other than that, other more conventional coverages would apply. In other words, your commercial coverage only applies in very limited circumstances.
For more info, see How 6-Month and 12-Month Auto Insurance Policies Differ